A note on the asymptotic reduction of the Hodgkin-Huxley equations for nerve impulses

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Abstract

The (standard) FitzHugh reduction of the Hodgkin-Huxley equations for the propagation of nerve impulses ignores the dynamics of the activation gates. This assumption is invalid and leads to an over-estimation of the wave speed by a factor of 5 and the wrong dependence of wave speed on sodium channel conductance. The error occurs because a non-dimensional parameter, which is assumed to be small in the FitzHugh reduction, is in fact large (≈18). We analyse the Hodgkin-Huxley equations for propagating nerve impulses in the limit that this non-dimensional parameter is large, and show that the analytical results are consistent with numerical simulations of the Hodgkin-Huxley equations. © 2005 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.

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Hinch, R. (2005). A note on the asymptotic reduction of the Hodgkin-Huxley equations for nerve impulses. Bulletin of Mathematical Biology, 67(5), 947–955. https://doi.org/10.1016/j.bulm.2004.11.007

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